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TEACHER NOTES – M&M® Distributing Topic: This lesson is designed to explore the concept behind and practice the distributive property. Objective: Given M&M’s, exploratory worksheets, and practice worksheets, students will demonstrate an understanding of the use of the distributive property by simplifying expressions and finding perimeter of rectangles. Time Table: This lesson is designed for a 50 minute class period. TEKS Focus: A.4.B Use the commutative, associative, and distributive properties to simplify algebraic expressions Additional TEKS: A.4.A Materials: M&M’s (Per Class: 15 baggies of 6 red, 3 yellow, 2 green, 10 blue, 6 brown, 9 orange) Worksheets provided Transparencies of all worksheets. Lesson Overview: This lesson is a review of the definition of multiplication as repeated addition in effort to provide the conceptual base for introducing the distributive property. The lesson uses visual representations to model the distributive property and then provides the students with time to practice these skills. Grouping: The M&M activity can be completed in pairs, and the practice problems can be completed in pairs or individually. Procedure: 1. Review Multiplication defined as repeated addition (NOTE: Parentheses mean Multiply). a. 3(4) 4 4 4 b. 7(2) 2 2 2 2 2 2 2 c. 4(2 6) 2 6 2 6 2 6 2 6 d. 2( x 3) x 3 x 3 2. Walk through the M&M® Distributing: Distributive Property Activity problem #1 as a class. a. Read word problem. b. Set up M&M’s. c. Write Algebraic Expression. d. Write out the repeated addition. e. Add the expressions. 3. Students complete M&M® Distributing: Distributive Property Activity problems #2, 3, 4, and 5 in pairs. Stop between each problem to discuss results. 4. Problem #5 will be impossible for the students to complete because they will not have enough M&M’s. ASK: “Do you see a pattern or a shortcut we could take instead of using repeated addition?” The answer you are looking for is “We could use multiplication instead.” 5. Thus, on #5, show them how to multiply one of the following two ways (or both). 12(6 g 8 y ) 12(6 g 8 y ) 6g 8 y 12(6 g ) 12(8 y ) 12 72 g 96 y 72 g 96 y 6. Students complete the 10 practice problems from M&M® Distributing: Distributive Property Practice in class either individually or in pairs (at the teacher’s discretion). 7. Check the 10 problems and go over questions. 8. Pass out the homework. Homework: M&M® Distributing: Distributive Property Homework Extensions: 1. If you do not want to use M&M’s, you can change all of the problems to x’s and use algebra tiles or just draw and color the M&M’s. 2. More problems over Geometry (Perimeter and Area) could be added to the practice problems and the homework for a geometry review. ALGEBRA 1 STUDENT NOTES KEY NAME: __________________________________ PER: __________ DATE: ____________ M&M® DISTRIBUTING Distributive Property Activity Represent each of the following situations using M&M’s. Then write as an algebraic expression. 1. three groups of 2 red and 1 yellow Algebraic Expression: 3(2r +1 y) Repeated Addition: 2r + 1y 2. two groups of 1 green and 5 blue Algebraic Expression: 2(1g + 5b) Repeated Addition: 2r + 1y + 2r + 1y Total: 6r + 3y 1g + 5b + 1g + 5b Total: 2g + 10b 3. three groups of 2 brown and 3 orange Algebraic Expression: 3(2b + 3o) Repeated Addition: 2b + 3o 4. two groups of 5 blue and 3 red Algebraic Expression: Repeated Addition: 2b + 3o 2(5b + 3r) 5b + 3r + 5b + 3r + 2b + 3o Total: Total: 5. 10b + 6r 6b + 9o twelve groups of 6 green and 8 yellow Algebraic Expression: 12(6g + 8y) 12(6g + 8y) 6g + 8y 12(6g) + 12(8y) x 72g + 96y 12 12(6g) + 12(8y) = 72g + 96y Total: 72g + 96y ALGEBRA 1 IN-CLASS PRACTICE KEY NAME: _________________________________ PERIOD: _________ DATE: _____________ M&M® DISTRIBUTING Distributive Property Practice Key The Distributive Property Words The product of a and (b + c) The product of a and (b – c) Let a, b, c be real numbers. Algebra Examples a(b c) ab ac 3(4 2) 3(4) 3(2) (b c)a ba ca (3 5)2 3(2) 5(2) a(b c) ab ac 5(6 4) 5(6) 5(4) (b c)a ba ca (8 6)4 8(4) 6(4) Directions: Please simplify the following expressions by using the distributive property. 1. 3(2 y 5) 3(2) y 3(5) 6 y 15 2. 2(8 h) 4. 7(5 x 10) 5. ( y x) 1( y ) 1( x) y x 7(5) x 7(10) 35 x 70 7. 2( x 4) 3 2 x 2(4) 3 2x 8 3 2x 5 3. (3 3x)(5) 2(8) 2h 3(5) 3(5) x 16 2h 15 15 x 8. 4( z 8) 3 z 2 4 z 4(8) 3 z 2 4 z 32 3 z 2 7 z 30 10. 11. A square has sides of length 3x 10. 5(c 3a 5t ) 8(d 2o g ) 5c 3(5)a 5(5)t 8d 8(2)o 8 g 3x 10 5c 15a 25t 8d 16o 8 g What is the perimeter of the square? p 4(3 x 10) p 12 x 40 6. (5 6 x)(2) 5(2) 6(2) x 10 12 x 9. 11(2 x 1) 4(7 3 x) 11(2) x 11( 1) 4(7) 4( 3) x 22 x 11 28 12 x 34 x 39 12. Find the area of the rectangle. 7x – 4 3 A = 21x – 12 ALGEBRA I NAME: HOMEWORK KEY DATE: PERIOD: M&M® Distributing Distributive Property Homework The Distributive Property Words Let a, b, c represent real numbers. Algebra Examples a(b c) ab ac 3(4 2) 3(4) 3(2) (b c)a ba ca (3 5)2 3(2) 5(2) a(b c) ab ac 5(6 4) 5(6) 5(4) (b c)a ba ca (8 6)4 8(4) 6(4) The product of a and (b + c) The product of a and (b – c) Use the distributive property to write equivalent expression. 2. 9(a b) 1. Find the area. b+7 2 2b 14 9a 9b 3. 8( y 2) 4. 3(2 w 7) 8 y 16 6w 21 5. 4(e 4) 6. (8 j )3 4e 16 24 3 j 7. (7 l )9 8. 4(a b c) 63 9l 4a 4b 4c 9. Find the perimeter. 3x 3 10. Find the perimeter. 4x 4 9x 9 3x 3 2x 2 3x 3 12 x 12 11. Find the area. 5x + 15 x+3 5 2x 2 4x 4 12. Find the perimeter of the regular octagon. 16x + 56 2x + 7 ALGEBRA 1 STUDENT NOTES NAME: _____________________________ PER: __________ DATE: ____________ M&M® DISTRIBUTING Distributive Property Activity Represent each of the following situations using M&M’s. Then write as an algebraic expression. 1. three groups of 2 red and 1 yellow Algebraic Expression: ________________ Repeated Addition: 3. two groups of 1 green and 5 blue Algebraic Expression: ________________ Repeated Addition: + Total: + Total: 3. three groups of 2 brown and 3 orange Algebraic Expression: ________________ Repeated Addition: 5. two groups of 5 blue and 3 red Algebraic Expression: ________________ Repeated Addition: + Total: 5. + Total: twelve groups of 6 green and 8 yellow Algebraic Expression: ________________ Total: ALGEBRA 1 IN-CLASS PRACTICE NAME: _________________________________ PERIOD: _________ DATE: _____________ M&M® DISTRIBUTING Distributive Property Practice The Distributive Property Words The product of a and (b + c) The product of a and (b – c) Let a, b, c be real numbers. Algebra Examples a(b c) ab ac 3(4 2) 3(4) 3(2) (b c)a ba ca (3 5)2 3(2) 5(2) a(b c) ab ac 5(6 4) 5(6) 5(4) (b c)a ba ca (8 6)4 8(4) 6(4) Directions: Please simplify the following expressions by using the distributive property. 1. 3(2 y 5) 2. 2(8 h) 3. (3 3 x)(5) 4. 7(5 x 10) 5. ( y x) 6. (5 6 x)(2) 8. 4( z 8) 3z 2 9. 11(2 x 1) 4(7 3x) 11. A square has sides of length 3x 10. What is the perimeter of the square? 12. Find the area of the rectangle 7. 2( x 4) 3 9. 5(c 3a 5t ) 8(d 2o g ) 3x 10 7x – 4 3 ALGEBRA I NAME: PERIOD: HOMEWORK DATE: M&M® Distributing Distributive Property Homework The Distributive Property Words Let a, b, c represent real numbers. Algebra Examples a(b c) ab ac 3(4 2) 3(4) 3(2) (b c)a ba ca (3 5)2 3(2) 5(2) a(b c) ab ac 5(6 4) 5(6) 5(4) (b c)a ba ca (8 6)4 8(4) 6(4) The product of a and (b + c) The product of a and (b – c) Use the distributive property to write equivalent expression. 2. 9(a b) 1. Find the area. b+7 2 3. 8( y 2) 4. 3(2 w 7) 5. 4(e 4) 6. (8 j )3 7. (7 l )9 8. 4(a b c) 9. Find the perimeter. 10. Find the perimeter. 3x 3 3x 3 11. Find the area. x+3 5 3x 3 4x 4 2x 2 2x 2 4x 4 12. Find the perimeter of the regular octagon. 2x + 7